Question:
Instantaneous power delivered to a damped harmonic oscillator (natural frequency is \( \omega_0 \)) by an external periodic force (driving frequency \( \omega \)) under steady state conditions is
Instantaneous power delivered to a damped harmonic oscillator (natural frequency is \( \omega_0 \)) by an external periodic force (driving frequency \( \omega \)) under steady state conditions is
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In steady state, external force supplies exactly the energy lost due to damping → net positive power.
Updated On: May 1, 2026
- positive always
- negative always
- positive and negative with power integrated over a period being zero
- positive and negative with power integrated over a period being positive
- positive and negative with power integrated over a period being negative
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The Correct Option is D
Solution and Explanation
Concept:
Power: \[ P = F \cdot v \] In damped oscillator under steady state, energy is continuously supplied to balance losses.
Step 1: Nature of instantaneous power
Since force and velocity can have different phases: \[ P \text{ can be positive or negative} \]
Step 2: Over one complete cycle
Energy lost due to damping must be compensated.
Step 3: Net effect
Average power over a cycle is positive. \[ \boxed{\text{Power is positive and negative but net over cycle is positive}} \]
Power: \[ P = F \cdot v \] In damped oscillator under steady state, energy is continuously supplied to balance losses.
Step 1: Nature of instantaneous power
Since force and velocity can have different phases: \[ P \text{ can be positive or negative} \]
Step 2: Over one complete cycle
Energy lost due to damping must be compensated.
Step 3: Net effect
Average power over a cycle is positive. \[ \boxed{\text{Power is positive and negative but net over cycle is positive}} \]
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